FOUNDATIONS OF QUANTUM MECHANICS

172 CHAPTER VIII. THE MEASUREMENT PROBLEM
preliminary to the measurement, a certain value A to the object system S, proves to be contagious;
after the interaction also the pointer quantity of the measuring apparatus has no definite value anymore,
and if the composite system SM is coupled to another measuring apparatus M ′ , this also
becomes infected with ‘property loss’. This is why (VIII. 16) and (VIII. 17) are preferred as final
states over (VIII. 15).
The problem of giving a treatment of the measurement process which produces one of these two
final states, and which therefore ‘creates’ the definite values by means of the measuring interaction,
is the measurement problem in the narrow sense. Notice that (VIII. 16) and (VIII. 17) cannot be
obtained from the initial state by means of a unitary transformation. Therefore, we have to adjust or
extend the first five Von Neumann postulates. We will discuss some proposals for a solution.
VIII. 4. 1
THE PROJECTION POSTULATE AND CONSCIOUSNESS
By adding the projection postulate to the first five postulates, p. 41, Von Neumann gave the standard
solution to the measurement problem in the narrow sense. He distinguished two ways in which
a state can change in time,
Process 1. The discontinuous, non - unitary, indeterministic projection occurring at a
measurement; the projection postulate.
Process 2. The continuous, unitary, deterministic evolution which is consistent with the
Schrödinger equation or its generalization to mixed states, as long as no measurement is
made on the system; the Schrödinger postulate.
At measurement the state undergoes a transition into the eigenstate belonging to the outcome of
measurement. Therefore, this brings about the final state (VIII. 17) and gives, in accordance with the
eigenstate-eigenvalue link, p. 170, definite properties to both the object system and the pointer of the
measuring apparatus.
Although the measurement problem in the narrow sense is solved with these two types of evolution,
the measurement problem in the broad sense, p. 164, comes into prominence more than ever.
We would now like to have an explanation for the particular nature of a measurement, or at least a
criterion with which it can be distinguished of other processes.
Such a criterion is provided, by Von Neumann and for instance Wigner, W. Heitler (1970 p. 42),
and F. London and E. Bauer (1939), in terms of the consciousness of an observer. London and Bauer
reason as follows.
Consider an object system S, a measuring apparatus M and a conscious observer B. The state of
the composite system after measurement is, according to (VIII. 11),
|Φ⟩ = ∑ j
c j |a j ⟩ ⊗ |r j ⟩ ⊗ |b j ⟩. (VIII. 18)
According to London and Bauer, this is the description of the state for us. But for the conscious
observer B it is not the same, because B has the characteristic capacity of introspection. By introspection
he knows in which eigenstate he is, he perceives one certain pointer position. This breaks the